Department of Mathematics, Statistics and Actuarial Sciences
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Item D-optimal Rotatable Central Composite Designs Constructed through Resolutions(Mathematical Theory and Modeling, 2016) Kinyua, Margaret; Koskei, Joseph; Kinyanjui, JosphatResponse surface methodology is widely used for developing, improving, and optimizing processes in various fields. A design is of resolution 𝑅 if no 𝑝 factors effect is confounded with any other effect containing less than 𝑅 −𝑝 factors. In this study, a method for constructing second order rotatable designs based on resolution R, in particular resolution III and IV for three and four factors respectively, argumented with star points is presented. Attention is given to the moment matrices and the related information surfaces based on the parameter subsystem of interest on the second-order Kronecker model and their corresponding rotatable Central Composite Designs (CCDs). Weighted Central Composite Designs (WCCDs) are derived by assigning different weights to two portions of the CCD namely the cube and star portion. The derived designs achieve the property of rotatability and high efficiency and are shown to be D-optimal. Experimental runs are reduced hence economical and the resulting designs are improved in terms of optimality and estimation efficiency. The results show that the cube portion is of great importance in D-optimal resolution III design while the two portions are of equall importance in resolution IV design.Item Multinomial Logit Modeling of Factors Associated With Multiple Sexual Partners from the Kenya Aids Indicator Survey 2007(American Journal of Theoretical and Applied Statistics, 2015-05) Kinyanjui, Josphat; Mwalili, Samuel; Ang’ir, BerylThe number of lifetime sex partners of an individual has an important effect on Human Immunodeficiency Virus (HIV) status of an individual; hence modeling multiple sexual partnerships is an essential component of any analysis of HIV outcome. Multiple sexual partnerships are associated with greater risk of HIV, Sexually Transmitted infections (STIs) and intimate partner violence. This research project presents a general approach for modeling logit of clustered (correlated) ordinal and nominal responses using polytomous data from the Kenya AIDS Indicator Survey 2007 (NASCOP 2010). We review multinomial logit models as generalized linear models. The model is applied to HIV prevalence data among men and women in Kenya, derived from the Kenya AIDS Indicator Survey 2007 (KAIS). We generalize logistic regression to handle multinomial response variables, with separate models for nominal and ordinal cases. When modeling a nominal response variable we are interested in finding if certain predictors have an effect on the probabilities. The baseline category logit model, models the odds of being in one category relative to being in a designated category (last category), for all pairs of categories. It is used for nominal responses. A maximum likelihood estimation (MLE) approach is used for baseline category logit model. To model an ordinal response variable one models the cumulative response probabilities or cumulative odds. The cumulative logit model is used when the response of an individual unit is restricted to one of a finite number of ordinal values. This study shows the practicality of multinomial logit model in analyzing epidemiological data. Other studies have found education to be associated with multiple sexual partners. In this study, we observed that multiple sexual partners is not related to education. Other covariates like Gender, Place of residence, sexually active individuals for the past 12 months and marital status were found to be associated with multiple sexual partners. Individuals that are sexually active for the past 12 months were found to be ten times more likely to have multiple sexual partners compared to those that are not. After controlling for all other factors, the odds of male to female having multiple sexual partners doubled to 7.6 meaning male are almost 8 times likely to have multiple sexual partners compared to female. Partner testing or couples testing is a main strategy of national testing initiatives in Kenya. Respondents are encouraged to learn their test results with their partner.